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In this paper, we find and develop a stochastic integral representation for the class of strictly stable distributions. We establish an explicit relationship between stochastic integral and shot-noise series representations of strictly stable distributions, which shows that the class of distributions representable by stochastic integral is larger than the class representable by a shot-noise series. This inclusion is proper when the stability index \(\alpha \) is greater than 1. We also give an explicit description of distributions possessing both representations.

Stochastic Integral and Series Representations for Strictly Stable Distributions